A274195 Decimal expansion of limiting ratio described in Comments.

1, 2, 9, 8, 6, 4, 0, 6, 4, 0, 8, 6, 1, 7, 0, 4, 6, 4, 5, 6, 9, 3, 3, 4, 4, 1, 6, 1, 5, 8, 5, 2, 8, 1, 2, 2, 0, 4, 8, 5, 5, 3, 9, 7, 7, 9, 8, 6, 5, 3, 7, 4, 5, 6, 3, 3, 1, 4, 5, 5, 4, 9, 3, 9, 2, 7, 3, 5, 7, 5, 5, 6, 3, 1, 8, 8, 7, 7, 3, 1, 4, 3, 1, 1, 2, 8

Offset

1,2

Comments

As in A274193, define g(n,k) = 1 for n >= 0; g(n,k) = 0 if k > n; g(n,k) = g(n-1,k-1) + g(n-1,3k) for n > 0, k > 1. The sum of numbers in the n-th row of the array {g(n,k)} is given by A274194, and "limiting ratio" = limit of A274194(n)/A274194(n-1).

Links

Table of n, a(n) for n=1..86.

Example

Limiting ratio = 1.2986406408617046456933441615...

Mathematica

z = 1500; g[n_, 0] = g[n, 0] = 1;
g[n_, k_] := g[n, k] = If[k > n, 0, g[n - 1, k - 1] + g[n - 1, 3 k]];
t = Table[g[n, k], {n, 0, z}, {k, 0, n}];
w = Map[Total, t];   (* A274194 *)
u = N[w[[z]]/w[[z - 1]], 100]
RealDigits[u][[1]] (* A274195 *)

Crossrefs

Cf. A274193, A274194, A274198, A274210 (reciprocal).

Sequence in context: A309211 A021339 A092971 * A021975 A192599 A021081

Adjacent sequences: A274192 A274193 A274194 * A274196 A274197 A274198

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jun 16 2016

Status

approved